In a known arrangement of this type the kinematic magnitudes of the web of material, such as displacement, speed and acceleration are detected by means of a measuring wheel rotating on the web of material. By means of this measuring wheel the detection is effected of analogue or digital signals corresponding to specific travel distances of the web of material, which are therefore proportional to the speed of the web of material, as a result of which, again, accelerations can be determined by the comparison of adjacent signals. Furthermore, a photosensor is provided which, on the printing of the web of material with print images, detects printed so-called registration marks, a registration mark being in each instance in a quite definite association with a print image. This photosensor therefore emits a signal which reproduces the position of the image at a particular point in time when actually the registration mark passes the sensor. The kinematic magnitudes detected by means of the measuring wheel are necessary in order to allow the effect to be felt of the displacement, the web speed and also speed changes which occur during the time from the detection of the registration mark to the cutting process. The detection of the kinematic magnitudes by means of a measuring wheel involves drawbacks, as the measuring wheel has mass inertia and, therefore, particularly on the accelerations of the web of material, produces errors. Furthermore, there occur errors of measurement by the measuring wheel as a consequence of diameter variations resulting from temperature fluctuations. In addition errors of measurement occur as a result of a slip between measuring wheel and web of material. To keep the slip as small as possible the measuring wheel must press the web of material with a specific application pressure, which again leads to compressions of the web of material which can detrimentally affect its appearance. In this connection it is also possible that surface structures of the measuring wheel, such as a knurling provided for reducing the slip, will be transferred to the web of material, damaging the latter. As a rule, the kinematic magnitudes are detected by the measuring wheel on the side of the web of material facing away from the print image; however, it is essential that the side of the web of material which has the print images should be cut exactly to the correct position, and thus in exact register. Furthermore, the measuring system integrated into the measuring wheel determines with its resolution power the achievable cutting length accuracy. These numerous drawbacks of the measuring wheel are countered by the fact that the generically pre-established overall process has given a good account of itself in practice.